Approximation methods for a common fixed point of a finite family of nonexpansive mappings

Habtu Zegeye, Naseer Shahzad

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Let K be a nonempty closed and convex subset of a real Banach space E. Let T: KE be a continuous pseudocontractive mapping and f:KE a contraction, both satisfying weakly inward condition. Then for t(0, 1), there exists a sequence {yt}K satisfying the following condition: yt=(1-t)f(yt)+tT(yt). Suppose further that {yt} is bounded or F(T) and E is a reflexive Banach space having weakly continuous duality mapping J for some gauge . Then it is proved that {yt} converges strongly to a fixed point of T, which is also a solution of certain variational inequality. Moreover, an explicit iteration process that converges strongly to a common fixed point of a finite family of nonexpansive mappings and hence to a solution of a certain variational inequality is constructed.

Original languageEnglish
Pages (from-to)1405-1419
Number of pages15
JournalNumerical Functional Analysis and Optimization
Volume28
Issue number11-12
DOIs
Publication statusPublished - Jan 1 2007

Fingerprint

Nonexpansive Mapping
Common Fixed Point
Approximation Methods
Variational Inequalities
Banach spaces
Duality Mapping
Converge
Pseudocontractive Mapping
Reflexive Banach Space
Contraction
Gauge
Fixed point
Banach space
Set theory
Iteration
Closed
Gages
Subset
Family

All Science Journal Classification (ASJC) codes

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

Cite this

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Approximation methods for a common fixed point of a finite family of nonexpansive mappings. / Zegeye, Habtu; Shahzad, Naseer.

In: Numerical Functional Analysis and Optimization, Vol. 28, No. 11-12, 01.01.2007, p. 1405-1419.

Research output: Contribution to journalArticle

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